Calculation of the quarkonium spectrum and mb, mc to order α4s

Abstract

We include two loop, relativistic one loop and second order relativistic tree level corrections, plus leading nonperturbative contributions, to obtain a calculation of the lower states in the heavy quarkonium spectrum correct up to, and including, O ( α 4 s ) and leading Λ 4 / m 4 terms. This allows us, in particular, to obtain a model-independent determination of the pole masses of the b,c quarks, m b = 5015 + 110 − 70 MeV , m c = 1884 + 222 − 133 MeV , to which correspond the ¯ MS masses m b ( m 2 b ) = 4453 + 50 − 32 MeV , m c ( m 2 c ) = 1547 + 169 − 102 MeV . The decay Γ ( → Υ e + e − ) is found to be in agreement with experiment, Γ ( → Υ e + e − ) = 1.135 + 0.27 − 0.29 keV ( expt . = 1.320 ± 0.04 keV ) , and the hyperfine splitting is predicted to be M ( Υ ) − M ( η ) = 48.5 + 15.7 − 12.2 MeV .